# Compound Interest

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## What is Compound Interest?

Compound interest is the resulting interest that is generated on the combination of the principal amount and the accumulated interest from previous periods.

With compound interest, money grows at an accelerated rate compared to simple interest, which is calculated only on the initial principal invested into the financial instrument. The more frequently interest is compounded, the faster the principal grows.

### Techopedia Explains Compound Interest Meaning

Compound interest is a fundamental concept used in different financial instruments such as savings accounts, investments, loans, and other financial products. It’s important because it allows money to grow at an increasing rate over time, making it a powerful tool for accumulating wealth or understanding the cost of borrowing money.

Understanding compound interest is crucial for both investors and borrowers, as it can have a significant impact on their financial outcomes. Investors can leverage compound interest to grow their wealth over time, while borrowers need to be mindful of its effects to avoid excessive interest costs.

## How Does Compound Interest Work?

Compound interest can grow a savings or investment account’s balance faster because, in addition to earning returns on your original investment or deposit amount – the principal – the account also earns a return on those accumulated gains.

For example, let’s say a person deposits \$1,000 into a savings account with a 5% interest rate, compounding annually.

In year one, the account would earn: \$1,000 x 0.05 = \$50

The new account balance at the end of year one would be: \$1,000 + \$50 = \$1,050

In year two, the interest would be calculated on the new higher balance of \$1,050, not the original \$1,000 deposit. So, the account would earn: \$1,050 x 0.05 = \$52.50

This would result in a final account balance of \$1,102.50 (\$1,050 + \$52.50) by the end of year two.

The easiest way to understand the powerful meaning of compound interest is to visualize how it can help money grow exponentially, not just linearly like with simple interest. This acceleration effect is even more dramatic and impactful over longer periods.

## How to Calculate Compound Interest?

The mathematical formula for calculating compound interest manually is as follows:

A = [P(1 + r/n)](nt)

Where:

A = Ending amount, including Interest.

P = Principal amount.

r = Annual interest rate as a decimal.

n = Compounding periods per year.

t = Investment horizon in years.

For example, if a customer deposits \$10,000 into an account earning 4% interest, compounding monthly for 5 years, the compounded interest calculation for that period will be as follows:

A = 10,000 * [(1 + (0.04/12))(12*5)] = \$12,683.06

As you can see, the formula gets complex quickly as more variables are added. Using a calculator is often the easiest way.

### Tools to Calculate Compound Interest

There are several tools, both online and offline, to help calculate compound interest returns:

• Spreadsheets: Microsoft Excel or Google Sheets have created compound interest formulas that allow users to easily draft estimates.
• Traditional Calculators: Financial calculators can compute compound returns. Many banks also offer compound interest calculators on their websites.
• Online Tools: Sites like Investor.gov and others provide access to a free compound interest calculator. They will require specific details like the applicable interest rate, compounding frequency, investment horizon, and additional recurring contributions to estimate the final balance that the account would reach after the compounding period ends.

### Online Compound Interest Calculators

Online calculators allow you to easily estimate compound returns by plugging in details like:

• Starting principal amount.
• Expected annual return.
• Investment timeframe.
• Compounding frequency (daily, monthly, annually).
• Regular contributions.

They work by using the mathematical compound interest formula explained above, but they do the heavy lifting behind the scenes. Advanced versions allow users to create detailed projections of investment growth over multiple years and model for different interest rate scenarios.

Here are a handful of online compound interest calculators that you can use:

• NerdWallet Online Compound Interest Calculator: this user-friendly calculator lets users estimate how much an investment or savings account balance would grow over time based on an initial deposit, interest rate, and periodical contributions. It has all the variables that one needs to draft robust projections.
• Investor.gov Compound Interest Calculator: This calculator is provided by a government site that educates investors and consumers about financial topics. It has all of the essential variables that one would need to draft projections but introduces an interesting “interest rate variance range” field that lets the user create various scenarios based on potential changes in the applicable rate.
• BankRate Compound Interest Calculator: BankRate is known for its useful ratings of credit cards, bank accounts, and other debt products. Its compound interest calculator is highly user-friendly and provides a chart that shows how much the account balance would grow over time based on an initial deposit and a set of periodical contributions.

## Compound Interest Investments

Now that we have explored an in-depth definition of compound interest, the following is a list of the types of accounts that commonly produce this type of return.

• High-Yield Savings: Online banks frequently offer savings accounts with daily compounding interest, allowing balances to grow faster. The most competitive accounts can offer annual percentage yields (APY) 6 or 7 times higher than the national average.
• Money Market Accounts: These savings accounts provide limited check writing ability while paying interest that compounds monthly or quarterly. Rates are often slightly higher than standard savings products.
• Certificates of Deposit (CDs): CDs pay lump-sum interest that compounds until maturity, which can range from 3 months to 5 years or more. However, early withdrawal penalties can impact gains.
• Retirement Accounts: Retirement and pension plans like 401(k)s allow pre-tax earnings to compound on a tax-deferred status over decades. IRA balances also benefit from decades of exponential tax-advantaged growth leading up to retirement.
• Stocks: Shares of public companies provide compound returns via escalating stock prices and dividend reinvestment plans paid on the shares. From 1996 to 2022, stocks have returned around 9% annually.
• Investment Funds: Mutual funds and exchange-traded funds (ETFs) own baskets of assets that provide compound earnings power passed through to investors. Low-cost index funds simplify compound investing.

### Compound Interest Investment Examples

Many banking and investment products leverage compound returns, including the following:

 Savings Accounts The interest earned on deposits compounds based on the terms offered by the account. High-yield online savings accounts frequently offer daily compound interest. CDs Certificates of deposit pay interest that compounds until maturity, often monthly or quarterly. Retirement Accounts 401(k)s, IRAs, and other tax-advantaged retirement accounts grow via compound earnings on the investments held. Investment Portfolios Stocks, bonds, mutual funds, and other similar investment vehicles generate compound returns from capital appreciation and reinvested dividends over long periods.

The earlier the money is put into vehicles generating compound returns, the more time it has to grow exponentially.

## The Rule of 72

The Rule of 72 offers a shortcut to estimate how quickly compound returns can double your money. Simply divide 72 by the annual interest rate you are being offered on any financial product. The result expresses how many years it will take to double your investment through compound growth alone.

For example, if your account is earning an 8% interest rate per year, dividing 72 by that number will give you 9 years (72/8=9 years). This means that money invested at an 8% compound rate would double in around 9 years typically.

## What’s the Difference Between Simple and Compound Interest?

Simple interest calculates returns based only on the initial principal amount invested or deposited. The account balance grows, but interest payments remain linear as they are calculated based on that initial amount and not the sum of both the principal and the interest paid.

Compound interest differs because it generates returns not only on the original principal but also on the accumulated interest and returns from previous periods. So, as interest accrues, it produces additional interest, fueling exponential growth of the total balance over time.

This is why long investment horizons for compound interest, like decades for retirement investing, have such an immense wealth-creation power. Short durations favor simple interest, but compounding wins if investors hold the investment for long enough.

• Accelerates returns exponentially over time.
• Maximizes growth the earlier money is invested.
• Little effort is needed once invested, interest earns more interest automatically.
• Available on many saving and investment products like savings accounts, certificates of deposit (CDs), and individual retirement accounts (IRAs).

• Works against the investor if they are paying the minimum installment on credit cards and loans.
• Compounding demands long holding periods to fully take advantage of its power.
• It can be difficult for the average person to manually calculate compound interest.

Compound interest turbocharges account balances by reinvesting earnings and interest to generate additional gains. Starting early, reinvesting all earnings, and giving compound returns enough time to work are key to building wealth.